Projecting a vector to another vector
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Victor
el 28 de Feb. de 2011
Respondida: Brandon O'Neill
el 26 de Mzo. de 2021
I would like to project a vector to another vector. You can find more information here:
For example I would like to project vector A to vector B. I have used these tricks but it does not work: Any comment is appreciated.
-----------------------
Solution 1)
A=[-10,10,0];
B=[0,0,1];
C=(dot(A,B)/norm(B)^2)*B
---------------------------------
Solution 2)
A=[-10,10,0];
B=[0,0,1];
CosTheta = dot(A,B)/(norm(A)*norm(B));
ThetaInDegrees = acos(CosTheta)*180/pi;
c=norm(A)*cos(ThetaInDegrees)
-----------------------------
1 comentario
Respuesta aceptada
Jan
el 1 de Mzo. de 2011
You have to tell DOT, that it must work on the 2nd dimension. Finally BSXFUN is needed to multiply the [88 x 1] and the [88 x 3] arrays. Unfortunalely NORM replies a matrix norm when operating on a matrix. Either use DNorm2: http://www.mathworks.com/matlabcentral/fileexchange/29035-dnorm2 or create the vector norm manually:
A = repmat([10,10,-10] ,[88,1]);
B = repmat([1,1,-1], [88,1]);
lenC = dot(A, B, 2) ./ sum(B .* B, 2); % EDITED, twice
C = bsxfun(@times, lenC, B)
4 comentarios
Más respuestas (9)
Paulo Silva
el 28 de Feb. de 2011
A=[-10,10,0];
B=[0,0,1];
%calculation of the projection of A into B
C=(sum(A.*B)/(norm(B)^2))*B;
%versors of each vector
An=A/norm(A);
Bn=B/norm(B);
Cn=C/norm(C);
%graphic representation
clf
line([0 A(1)],[0 A(2)],[0 A(3)],'LineWidth',10,'Color',[0 0 1])
line([0 B(1)],[0 B(2)],[0 B(3)],'LineWidth',8,'Color',[0 1 0])
line([0 C(1)],[0 C(2)],[0 C(3)],'LineWidth',5,'Color',[1 0 0])
legend('A','B','proj A into B')
xlabel('X')
ylabel('Y')
zlabel('Z')
view(80,10)
5 comentarios
Jan
el 1 de Mzo. de 2011
What exactly does "but it does not work" mean?
Your solution 1:
A = [-10,10,0];
B = [0,0,1];
C = (dot(A,B)/norm(B)^2)*B
This looks ok. If you get C = [0,0,0], the method works. A and B are orthogonal, such that the projection is zero.
Your solution 2: wrong
CosTheta = dot(A,B)/(norm(A)*norm(B));
ThetaInDegrees = acos(CosTheta)*180/pi;
c=norm(A)*cos(ThetaInDegrees)
Now c is a scalar, but you wanted a vector. Converting Theta in degrees is not correct here: COS works win radians. Use COSD for degerees. Improved:
CosTheta = dot(A,B) / (norm(A)*norm(B));
C = norm(A) * CosTheta * B / norm(B);
And as expected: If you insert CosTheta in the 2nd line, you get your solution 1 again.
2 comentarios
Paulo Silva
el 1 de Mzo. de 2011
I failed somehow to find the function dot and done sum(A.*B) instead :) but the results are the same
Jan
el 1 de Mzo. de 2011
sum(A.*B) and A*B' are faster then DOT. But for [1 x 3] vectors this does not matter.
Foday Samura
el 1 de Mayo de 2020
Find the length (or norm) of the vector that is the orthogonal projection of the vector a = [ 1 2 4 ] onto b = [6 10 3 ]. Type an answer that is accurate to 3 decimal places. (For example, if your answer is 4+2/3, you should type 4.667).
0 comentarios
fatema hasan
el 13 de Dic. de 2020
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fatema hasan
el 13 de Dic. de 2020
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fatema hasan
el 13 de Dic. de 2020
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0 comentarios
fatema hasan
el 13 de Dic. de 2020
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Brandon O'Neill
el 26 de Mzo. de 2021
At a certain time of day the radiant energy from the sun reaches the roof along the direction given by the unit vector
The fraction of the sun’s energy which is falling perpendicularly on the roof is the projection of vector (A) onto the direction perpendicular to the roof – this is the dot product of (A) with the unit vector.
Q1) Use Matlab to calculate the fraction of the sun’s energy which is falling perpendicularly on the roof.
can anyone help with this?
the univ vector is [0.7627;0.5509;0.3390]
the vector A = 1/sqrt(21)[1;2;-4]
0 comentarios
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